Hallenrm and pgrmdave:
I might be wrong, but I think there is a misunderstanding of what I mean by an 'argument'. An argument is not a quarrel between two people (the way I mean it).
An argument is a conclusion drawn from the available facts. Each side usually has various 'arguments' that may support them.
Eg, a scientific / mathematical argument: the sum of the sides of a hypotinuse is equal to the SUM of the sides. The argument is "one can split the hypotinuse into a series of steps. The length is the sum of the sides. Now if you make infinitly small steps, the limit is a straight line so the length of the hypotinuse is the sum of the steps". NOTE THIS ARGUMENT IS WRONG (bonus marks if you can spot the flaw). This illustrates how an argument can be wrong even though it looks right at first.
Wikipedia has a good section on it. But the problem is that it's approach is far too logical and philosophical. I want to stay clear of the philosophical and get something concrete and usable in practice.
What do you guys do? You hear a debate between two sides. Which arguments to you dismiss and which do you accept? Why? How do you 'test' them?